Evaluate (-8+ square root of -20)/24

Problem

(−8+√(,−20))/24

Solution

1. Simplify the square root of the negative number by using the imaginary unit i where √(,−1)=i

√(,−20)=√(,−1⋅4⋅5)

√(,−20)=2*i√(,5)

2. Substitute the simplified radical back into the original expression.

(−8+2*i√(,5))/24

3. Factor out the greatest common factor from the terms in the numerator.

2*(−4+i√(,5))

4. Divide the numerator and the denominator by their greatest common divisor, which is 8 for the whole expression or 2 for the factored term.

(2*(−4+i√(,5)))/24=(−4+i√(,5))/12

5. Split the fraction into its real and imaginary parts to write it in standard form a+b*i

(−4)/12+(i√(,5))/12

−1/3+√(,5)/12*i

Final Answer

(−8+√(,−20))/24=−1/3+√(,5)/12*i

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